The present invention relates to non-contact topographical analysis apparatus and a method thereof and in particular to the generation of Makyoh topograms enabling quantitative measurement of variations in the mirrored surface of an object. The present invention is particularly concerned, but not exclusively, with the simultaneous measurement of the reflectivity and height variations of a large mirror-polished surface, such as defects in semiconductor wafer surfaces.
For the current generation of microelectronic circuits, the manufacturing process requires perfectly flat large diameter semiconductor wafers. There is a well-defined need for characterisation techniques that can accurately assess the polishing quality of these wafers and can be used as quality control and production line monitoring tools providing qualitative pass/fail type information and also as troubleshooting tools providing detailed and accurate quantitative information.
It has been known for some time that when a collimated beam of light is reflected by an approximately flat mirror-polished object and a screen is placed in the path of the reflected beam some distance away from the object, a xe2x80x98mirror imagexe2x80x99 of the object is formed on the screen. For a perfectly flat object with uniform reflectivity, the light intensity in the xe2x80x98mirror imagexe2x80x99 would be substantially uniform with some small variations due to edge diffraction effects close to the perimeter of the object. However, for objects with surface height variations, the xe2x80x98mirror imagexe2x80x99 no longer has a uniform intensity distribution. Even small height variations in the surface of the object will show up strongly amplified as dark or bright patches/lines in the xe2x80x98mirror imagexe2x80x99. xe2x80x98Mirror imagesxe2x80x99 of this type are called Makyoh topograms or xe2x80x98magic mirror imagesxe2x80x99. Makyoh topography has been used for a number of years as a tool for the inspection of mirror-polished surfaces, and in particular as a quality control tool for the assessment of semiconductor wafer surfaces.
In FIG. 1 a conventional Makyoh topograph is shown schematically. Light from a laser 1, or a bright lamp with a narrow bandpass filter, is homogenised using a diffuser, fly""s eye optics, or spatial filter assembly 2. A collimator lens 3 then forms an approximately parallel light beam, which in turn is reflected by the object 0 under test. The reflected beam is intersected either by a screen 4 for direct viewing or by a film or electronic camera for image recording. The object-camera distance is fixed and normally is in the range of 0.5 m to 2 m.
Typical Makyoh topograms from three different mirror-polished InP wafers are shown in FIGS. 2a, 2b and 2c. In FIG. 2a the image contrast is rather complex with the following main components: curved approximately parallel lines probably corresponding to saw or lapping marks; concentric circles in the centre of the image probably corresponding to growth striation lines; dark lines with cellular geometry probably corresponding to surface ridges caused by uneven mounting wax distribution during polishing; and dark and bright spots probably corresponding to mounds and dimples respectively. The wafer shown in FIG. 2b is of better overall quality, the only features revealed in the topogram are concentric circles in the centre and a small number of bright spots at random positions. Finally, the wafer shown in FIG. 2c is of excellent quality only exhibiting some very faint low contrast lines and spots. These images provide a qualitative measure of wafer polishing quality, however it is not possible to extract the actual height of the ridge network revealed in FIG. 2a or the depth of the dimples in FIG. 2b. As demonstrated by these images, conventional Makyoh topograms can be a very powerful tool for qualitative comparison, but they provide no quantitative information and the interpretation of the image contrast can be very complicated.
U.S. Pat. No. 4,547,073 describes apparatus for generating Makyoh topograms that includes a convex lens for converging light reflected from the object in order to project a defocussed image on the screen. With the apparatus described in U.S. Pat. No. 4,547,073 the distance between the object and the screen is reduced, in comparison to apparatus that does not employ a convex lens thereby making the apparatus more convenient for industrial use. A geometrical optics explanation is provided as to how the variations in surface height result in changes in intensity in the mirror image. However, the explanation is very general relying as it does on equating variations in surface height solely to a concave/convex mirror effect. This document provides no assistance as to how a quantitative analysis of the Makyoh topograms might be achieved.
The main drawbacks of Makyoh topography as described above are: Ambiguity in the interpretation of the topograms: almost identical Makyoh topograms can result from an object with some given surface height profile and constant reflectivity; an object with constant surface height and a given non-uniform reflective or an object with both height variations and a non-uniform reflectivity profile.
Lack of quantitative interpretation of the topograms.
The present invention seeks to provide improved topographical analysis apparatus and a method thereof that at least improves and in many cases overcomes the disadvantages described above with conventional Makyoh topography and in particular enables a quantitative interpretation of Makyoh topograms generated with the present invention.
The present invention provides a topographical analysis method for measuring variations in reflectivity or surface height of a reflective object comprising: illuminating a reflective surface of the object with a beam of light; recording with a recording device a plurality of images of the surface of the object generated by light reflected from the surface in which each image has a predetermined optical transformation with respect to every other image; measuring the light intensity distribution in each of the images generated by the reflected light; and determining and outputting at least one of the reflectivity and the relative surface height of the reflective surface of the object by predicting the reflectivity and relative surface height of an initial theoretical surface, iteratively adjusting the theoretical surface until the calculated light intensity distributions for the theoretical surface, corresponding to the optical transformations of each of the recorded images, converge with the recorded images.
Preferably the theoretical surface is adjusted by cyclical substitution of the calculated image intensity for the theoretical surface with the detected image intensity of each one of the images generated by the reflected light. In the preferred embodiment the light distribution of the theoretical surface is deemed to have converged when the difference between the calculated image intensity and the detected image intensities is less than a predetermined threshold.
In one embodiment of the present invention the plurality of images are recorded each at a different distance from the reflective surface of the object. The recording device may be moved to different positions along the optical axis of the reflected light to sequentially record the plurality of images. Alternatively, the reflected light may be divided into a plurality of portions with each portion of the reflected light being directed to a separate recording device in which the path length from the reflected surface of the object to each recording device is different. In a further alternative the effective path length between the object and the recording device may be altered by adjusting any optical elements located between the object and the recording device.
In a further or alternative embodiment the image generated by the reflected light is recorded at a plurality of different, distinct wavelengths. Additional optical elements may be provided for modifying (e.g. collimating) the incident beam of light. Where such additional elements are provided, the elements may be adjustable to enable the plurality of images each with a different optical transformation to be generated.
In a second aspect the present invention provides topographical analysis apparatus for measuring variations in the reflectivity or surface height of a reflective object comprising an optical system for directing a beam of light to a reflective surface of the object; a first recording device for recording a first image of the surface of the object generated by light reflected from the surface; at least one further recording device for recording one or more further images of the surface of the object, thereby generating a plurality of images in which each image has a predetermined optical transformation with respect to every other image: and an analyser for measuring the light intensity distribution in each of the plurality of images and for determining and outputting at least one of the reflectivity and the relative surface height of the reflective surface of the object by iteratively adjusting a theoretical surface, having an initial predetermined reflectivity and surface height, until the calculated light intensity distributions for the theoretical surface, corresponding to the optical transformations of each of the recorded images, converge with the recorded images.
Ideally, the analyser further includes a thresholding device for monitoring the difference between the calculated image intensity of the theoretical surface and the recorded image intensities and for determining that the theoretical surface substantially corresponds to the surface of the reflective object when the difference is less than a predetermined value.
The light source may be one or more narrow band-width sources such as lasers etc. Also, the first and the one or more further recording devices may be electronic cameras.
In one embodiment the first recording device and the one or more further recording devices is a single camera mounted on a moveable support for positioning the camera at different distances from the reflective surface of the object.
In a further or alternative embodiment the first and one or more further detector devices are wavelength specific and each is sensitive to a different distinct wavelength.
In a further aspect the present invention provides phase extraction software on a data carrier for determining variations in reflectivity or surface height of a reflective object, the software being programmed to perform the following steps: storing the measured light intensity distributions of a plurality of images of a reflective object in which each image has a predetermined optical transformation with respect to every other image; predicting the reflectivity and relative surface height of an initial theoretical surface and calculating the light intensity distribution for the theoretical surface; and iteratively adjusting the theoretical surface until the calculated light intensity distributions for the adjusted theoretical surface, corresponding to optical transformations of the stored images, converge with the stored light intensity distributions.
With the present invention, optical apparatus is provided for the recordal of more than one Makyoh topogram from the same object. The topograms are generated in such a way that the light intensity distributions resulting in the different topograms are subject to well-defined and different optical transformations (e.g. phase dispersion) on travelling from the object to the recording device. The quantitative interpretation of a set of such topograms then becomes a phase retrieval problem that can be solved using iterative numerical algorithms. With the present invention iterative Fourier transform techniques are employed that, where possible, are used to obtain a unique solution for the object reflectivity and surface height (phase) distributions.
Embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which: